Abstract:
We investigate existence and uniqueness conditions for solution to one Robin type problem for inhomogeneous biharmonic equation in the unit ball. We construct polynomial solution to the problem when the boundary functions of the problems are polynomials.
Keywords:
biharmonic equation, Robin type problem, harmonic polynomials, solvability conditions, polynomial solutions.
Citation:
V. V. Karachik, “Solving a problem of Robin type for biharmonic equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 2, 39–53; Russian Math. (Iz. VUZ), 62:2 (2018), 34–48
\Bibitem{Kar18}
\by V.~V.~Karachik
\paper Solving a problem of Robin type for biharmonic equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 2
\pages 39--53
\mathnet{http://mi.mathnet.ru/ivm9329}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 2
\pages 34--48
\crossref{https://doi.org/10.3103/S1066369X18020056}
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Linking options:
https://www.mathnet.ru/eng/ivm9329
https://www.mathnet.ru/eng/ivm/y2018/i2/p39
This publication is cited in the following 5 articles:
Abdelhak Hadj, “Stability Estimates in Determining Robin Coefficients for Biharmonic Inverse Problem”, Iran J Sci, 2025
A. A. Klyachin, “On $C^1$-convergence of piecewise polynomial solutions to a fourth order variational equation”, Ufa Math. J., 14:3 (2022), 60–69
A. Hadj, H. Saker, “Integral equations method for solving a biharmonic inverse problem in detection of Robin coefficients”, Appl. Numer. Math., 160 (2021), 436–450
D. Amanov, G. Ibragimov, A. Kilicman, “On a generalization of the initial-boundary problem for the vibrating string equation”, Symmetry-Basel, 11:1 (2019), 73
Petar Popivanov, RENEWABLE ENERGY SOURCES AND TECHNOLOGIES, 2161, RENEWABLE ENERGY SOURCES AND TECHNOLOGIES, 2019, 030028
Citation in format AMSBIB
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